The Physics of Falling Leaves

So far this semester, we’ve imagined objects falling down without any change in their course as they fall. You drop a ball straight down, it accelerates at 9.8 m/s² and that’s that. You drop something at an angle, same deal: separate the components, find horizontal and vertical acceleration, you all know how it goes. However, not everything seems to fall so perfectly. Take for example a feather, or a piece of paper. Those definitely do not fall at the same rate as a regular old ball. These objects seem to flutter, moving to the left and right as they fall down slowly. With the colors changing and the leaves falling, I was inspired to ask the question: why do leaves fall as they do?

            So how do we figure out the physics behind falling leaves? By experimentation in simplified systems of course! At a lab in the Weizman Institute of Science in Israel, scientists built a thin glass tank in order to represent a two-dimensional system, which they filled with liquid. They then dropped thin strips of metal or plastic into the tank and observed their motion as they fell down. They found two types of motion: “flutter” in which the object moved back and forth as it fell down, and “tumble” in which the strips rotated end over end. They discovered through their theoretical model that this motion was dictated by a constant, the Froude number. This number also predicts the motion sailing vessels, and the maximum speed a two- or four-legged animal can reach while walking before their motion turns into a run or gallop.

Froude's number: u₀ = characteristic flow velocity, g₀ = general characteristic of the external field (usually related simply to gravity), l₀ = characteristic length

For leaves, this number defines the relationship between the size of an object and its weight: longer objects flutter, shorter objects tumble. Therefore, long and light leaves take this flutter pathway when falling, which slows down its fall compared to it falling and accelerating from just gravity alone.  

Sources:

https://www.engineeringtoolbox.com/froude-number-d_578.html
https://wis-wander.weizmann.ac.il/space-physics/physics-falling-leaves